Characteristics of Local Pion–Nucleus Potentials That Are Equivalent to Kisslinger-Type Potentials

Johnson, Mikkel B.; Satchler, G.R.

doi:10.1006/aphy.1996.0054

Cited by 38 publications

(83 citation statements)

References 26 publications

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“…First one has to be aware that two different but phase-equivalent optical potentials might yield the same elastic scattering cross section, but lead to a different behavior of the pion wave function in the nuclear interior [45]. Since in Eq.…”

Section: B Dwiamentioning

confidence: 99%

Coherent photoproduction of pions on spin-zero nuclei in a relativistic, non-local model

1998

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A relativistic and non-local model for the coherent photoproduction of pions on spin-zero nuclei is presented. The production operator is derived from an effective Lagrangian model that contains all the degrees of freedom known to contribute to the elementary process. Using the framework of DWIA, the matrix elements of this operator are evaluated using relativistic bound state wave functions. Final state interactions are accounted for via a pion-nucleus optical potential. The effects of in-medium modifications of the production operator are discussed. We give results for 12 C and 40 Ca, and compare our calculations to the data of the A2 collaboration at MAMI.

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Section: B Dwiamentioning

confidence: 99%

Coherent photoproduction of pions on spin-zero nuclei in a relativistic, non-local model

1998

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“…The earliest works on pion-nucleus interaction were done using very limited data summarized in [4] [5]. The low-energy pion-nucleus elastic scattering data available at that time were primarily limited to forward angles and analyzed within the framework of non-local Kisslinger [6], local Laplacian [7] and localequivalent of Kisslinger [8] potentials. All these theoretical models however, had only a limited success in explaining subsequent data taken at large angles.…”

Section: Introductionmentioning

confidence: 99%

Analyses of <i>π</i><sup>±</sup> - 12C Elastic Scattering and Reaction Cross-Section Data Below, Atop and Above the Δ-Resonance

Shehadeh¹

2014

JMP

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The pion-nucleus elastic scattering and reaction cross-section data at incident energies below, atop and above the Δ-resonance are analyzed using the full Klein-Gordon equation using an optical potential. Analytic forms of the potential are determined using the inverse scattering theory in those cases where phase shift analyses were available. The Coulomb effect is incorporated using Stricker's prescription. Both elastic scattering data and the reaction cross sections between 120 and 400 MeV are well reproduced. Both real and imaginary parts of the potential are local. The potential points determined by the inverse scattering theory in the interior region at 230 MeV clearly establish that the real part is repulsive. This remains the case at higher incident energies. The real part turns repulsive above the resonance, whereas the imaginary part reflects the dominance of surface absorption, which is maximum near atop the Δ-resonance and then falling off at higher energies.

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“…The Kisslinger nonlocal potential [2] is: where, ω is the total energy of the pion in the center of mass (c.m.) system, the quantities q and α(r) mainly result from the s-and p-waves of the pion-nucleon interaction and they are complex and energy dependent and given in detail by Johnson and Satchler [4] . Recently, Johnson and Satchler [4] used the KrellEricson transformation [5] , which leads from the KleinGordon equation for pion scattering to a local potential for the transformed wave function, equivalent to Kisslinger nonlocal potential.…”

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confidence: 99%

“…system, the quantities q and α(r) mainly result from the s-and p-waves of the pion-nucleon interaction and they are complex and energy dependent and given in detail by Johnson and Satchler [4] . Recently, Johnson and Satchler [4] used the KrellEricson transformation [5] , which leads from the KleinGordon equation for pion scattering to a local potential for the transformed wave function, equivalent to Kisslinger nonlocal potential. This local potential was used to successfully analyze the elastic scattering of π ± from 12 C, 16 O, 28 Si and 40,44,48 Ca in the pion kinetic energy range of 30 to 292 MeV [6] .…”

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confidence: 99%

“…The aim of the present work is to calculate the angular distributions of the differential cross-sections of the π ± elastically and inelastically scattered to the lowest 2 + and 3 -states in 12 C in the energy range of 50 to 260 MeV, using three independent methods of π ± -nucleus optical potential, the 3α-particle model of the nucleus [1] , the local-equivalent Kisslinger potential [4] and the Laplacian local potential [3] . The results of the three calculations are compared to the experimental data [9,10] .…”

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Different Methods for Pion-nucleus Optical Potential

Khallaf¹,

Ebrahim²

2005

American J. of Applied Sciences

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Elastic and inelastic cross-sections for pion scattering on 12 C at pion kinetic energy ranging from 50 to 260 MeV are computed using three independent methods of π ± -nucleus optical potential, the 3α-particle model of the nucleus, the equivalent local Kisslinger potential and the Laplacian one. Reasonable fits to the measured values are obtained for 12 C without adjusting free parameters. The ability of these methods to account for elastic, inelastic, total and reaction cross-section data are somewhat similar. The Kisslinger-based local potential is the more suitable for describing the elastic and inelastic cross-sections of π ± -nucleus scattering. It seems that the 3α-particle model of 12 C is not useful in the description of pion scattering on 12 C at least in the ∆-resonance region.

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Characteristics of Local Pion–Nucleus Potentials That Are Equivalent to Kisslinger-Type Potentials

Cited by 38 publications

References 26 publications

Coherent photoproduction of pions on spin-zero nuclei in a relativistic, non-local model

Coherent photoproduction of pions on spin-zero nuclei in a relativistic, non-local model

Analyses of <i>π</i><sup>±</sup> - 12C Elastic Scattering and Reaction Cross-Section Data Below, Atop and Above the Δ-Resonance

Different Methods for Pion-nucleus Optical Potential

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Characteristics of Local Pion–Nucleus Potentials That Are Equivalent to Kisslinger-Type Potentials

Cited by 38 publications

References 26 publications

Coherent photoproduction of pions on spin-zero nuclei in a relativistic, non-local model

Coherent photoproduction of pions on spin-zero nuclei in a relativistic, non-local model

Analyses of &lt;i&gt;π&lt;/i&gt;&lt;sup&gt;&#177;&lt;/sup&gt; - 12C Elastic Scattering and Reaction Cross-Section Data Below, Atop and Above the Δ-Resonance

Different Methods for Pion-nucleus Optical Potential

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Analyses of <i>π</i><sup>±</sup> - 12C Elastic Scattering and Reaction Cross-Section Data Below, Atop and Above the Δ-Resonance